As I mentioned, do a comparison of the Business fares you usually book / buy. Anything that is "promotional" like SQ D or U, I think (need to validate via SQ & LH calculators) earns more or similar in SQ KF. Once you buy C, Z, J fares on SQ, I think more award miles can be earned in LH M&M under the current scheme.

Of course, it depends whether you care to optimize the award mileage earnings or not. Once you hit KF Elite (even Silver) and then onwards, you'll earn mileage bonus in KF as well so it may balance out going for SQ KF all out and not even crediting anything to LH M&M. YMMV.

Also at least from Winter 2022/23 schedule onwards (end Oct 2022), LH has loaded F fares again for LH778/779 so at that stage, not sure you'll switch back to LH F from SQ C.